The use of acoustic (e.g., audible and/or ultrasonic) measurement systems in prior art downhole applications, such as logging while drilling (LWD), measurement while drilling (MWD), and wireline logging applications is well known. Such acoustic measurement systems are utilized in a variety of downhole applications including, for example, borehole caliper measurements, measurement of drilling fluid properties, and the determination of various physical properties of a formation. In one application, acoustic waveforms may be generated at one or more transmitters deployed in the borehole. The acoustic responses may then be received at an array of longitudinally spaced receivers deployed in the borehole. Acoustic logging in this manner provides an important set of borehole data and is commonly used in both LWD and wireline applications to determine compressional and shear wave velocities (also referred to as slownesses) of a formation.
It will be appreciated that the terms slowness and velocity are often used interchangeably in the art. They will likewise be used interchangeably herein with the understanding that they are inversely related to one another and that the measurement of either may be converted to the other by simple mathematical calculations. Additionally, as used in the art, there is not always a clear distinction between the terms LWD and MWD. Generally speaking MWD typically refers to measurements taken for the purpose of drilling the well (e.g., navigation) whereas LWD typically refers to measurement taken for the purpose of analysis of the formation and surrounding borehole conditions. Nevertheless, these terms are herein used synonymously and interchangeably.
Procedures for determining compressional and shear wave velocities are known in the prior art. In so-called “fast” formations, in which the shear wave velocity in the formation is greater than a compressional wave velocity in the drilling fluid (drilling mud), the compressional and shear wave velocities may be directly determined from the received waveforms by well established techniques. However, in so-called “slow” formations, in which the shear wave velocity of the formation is less than the compressional wave velocity of the drilling fluid, direct determination of the shear wave velocity is typically not possible since the shear waves in the formation do not generally refract back into the borehole. Nevertheless, the shear wave velocity remains an important parameter and its determination is desirable. As such, indirect methodologies have been developed to determine shear wave velocity in acoustically slow formations.
In conventional wireline logging applications, broad bandwidth, dipole logging tools were developed to indirectly measure shear wave velocity in acoustically slow formations. Dipole acoustic waves that travel along the formation (also referred to as flexural waves or first azimuthal order harmonics) are known to asymptotically approach the formation shear wave velocity at low frequencies (e.g., from about 1 to about 3 kHz). Thus, in conventional wireline acoustic logging applications, the formation shear wave velocity may be determined from the low frequency portion of the dipole waveform. A correction may then be applied to account for the adverse effect of residuals. Unfortunately, such dipole logging techniques are not typically suitable for LWD applications owing to potentially significant tool wave interference. In wireline applications, such tool waves may be reduced via various tool configurations, such as slotted sleeves, isolation joints, and flexible tool structures. In LWD, tool waves tend to be carried by the comparatively stiff tool body, which is essentially the drill string, and thus tend not to be easily mitigated. Additionally, the presence of the drill string in the borehole and tool eccentricity in the borehole tends to alter the propagation modes of the acoustic energy. Further, drill bit noise tends to significantly reduce the signal to noise ratio in the low frequency range of interest (where flexural waves travel at about the same velocity as the formation shear waves). As such, deriving formation shear wave velocities from LWD data is not nearly as straightforward as in wireline applications.
In order to overcome such limitations, there is a trend in the art towards attempting to use broadband quadrupole waveforms in LWD applications (see, for example, Tang, et al., in Petrophysics, vol. 44, pgs. 79–90, 2003). Such quadrupole waveforms (also referred to as screw waves or second order azimuthal harmonics) have been shown, for some configurations, to have a cut-off frequency below which tool wave propagation is substantially eliminated. It is thus apparent in the prior art that the use of quadrupole acoustic signals may be advantageous for determining shear wave velocities in LWD applications. However, the use of quadrupole waveforms tends to introduce other potential difficulties. For example, generating and receiving a relatively pure quadrupole acoustic signal typically requires complex segmented transmitters and receivers, which tend to be expensive. Such transmitters and receivers typically further require highly precise phasing (timing) of the various segments to produce relatively pure quadrupole acoustic signals and to suppress other modes (e.g., monopole and dipole). The difficulty in generating such acoustic signals may be further exacerbated by tool eccentricity in the borehole (e.g., in highly deviated wells in which the tool is typically lies on the low side of the borehole). Moreover, the use of such complex transmitters and receivers in severe downhole conditions including extreme temperatures and pressures, severe mechanical shocks and vibrations (up to 650 G per millisecond) tends to reduce tool reliability.
Therefore, there exists a need for improved methods for determining a shear wave velocity of a subterranean formation that address one or more of the shortcomings described above. Such methods may, for example, be advantageous in analysis of acoustically slow formations. In particular, it will be appreciated that a method that is not dependent on isolating dipole or quadrupole waveforms (for example), in the transmission or reception thereof, would be highly advantageous, since many of the above stated disadvantages would thus be obviated.